Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor. (c) 2007 American Institute of Physics

Stretched-exponential behavior and random walks on diluted hypercubic lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Kinetics of the polarization reversal process in a non-constant applied electric field and the generalized superposition principle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solvatationsdynamik: lokales Relaxationsverhalten glasbildender Systeme

In dieser Arbeit wurde das lokale Relaxationsverhalten niedermolekularer glasbildender Materialien mit der Methode der Solvatationsdynamik untersucht. Bei dieser Methode werden phosphoreszente Farbstoffe als molekulare Sonden für die lokale Dynamik im Glasbildner eingesetzt. Je nach verwendeter Sonde sind unterschiedliche Eigenschaften zugänglich:Mit Farbstoffen, die ihr Dipolmoment bei optischer Anregung nicht ändern, wird eine mechanische Solvatation gemessen, die die lokale viskoelastische Antwort des Materials widerspiegelt. Mit Farbstoffen, die eine Änderung des Dipolmoments bei optischer Anregung aufweisen,sind zusätzlich lokale dielektrische Eigenschaften des Materials zugänglich, die bei endlicher Polarität des Lösungsmittels dominieren. Das heterogene Relaxationsverhalten des Glasbildners 2-Methyltetrahydrofuran wurde quantitativ untersucht.Auf einem Temperaturbereich, auf dem die mittlere Relaxationszeit um mehr als 4 Dekaden variiert, konnte gezeigt werden, daß die Relaxation lokal rein exponentiell verläuft. Zur Abschätzung von Reichweiteneffekten wurden Solvatationsmessungen in einschränkenden Geometrien in Form von porösen Sol-Gel Gläsern mit Porendurchmessern zwischen 7,5-2,5 nm durchgeführt. Der Einfluß der Beschaffenheit der Porenoberfläche wurde durch Vergleichzwischen der Solvatation in nativen und in silanisierten Gläsern untersucht. Es wurde gezeigt, daß auch in den kleinsten verwendeten silanisierten Poren alle Charakteristika des jeweiligen Bulk-Systems erhalten bleiben.In den nativen porösen Gläsern dagegen führt der Einfluß der stark polaren Oberfläche zu einer Änderung der Dynamik.

Messung dynamischer Prozesse in der Nähe von Grenzflächen mit Hilfe neu entwickelter Lichtstreumethoden

Die vorliegende Arbeit behandelt die Entwicklung und Erprobung zweier neuer dynamischer Lichtstreumethoden: Die Resonanz verstärkte Lichtstreuung (REDLS: resonance enhanced dynamic light scattering) und die Wellenleiter verstärkte Lichtstreuung (WEDLS: waveguide enhanced dynamic light scattering). Beide Methoden verwenden eine Kombination aus evaneszenten Wellen und dynamischer Lichtstreuung: Bei der REDLS-Technik wird das evaneszentes Feld eines Oberflächenplasmons verwendet, bei der WEDLS-Technik handelt es sich um das evaneszente Feld von Metallfilm verstärkten Leckwellenleitermoden. Die neuen Methoden liefern Informationen über die Dynamik an Grenzflächen über ein breites Zeitfenster (einige Nanosekunden bis hin zu mehreren Sekunden) mit einer räumlichen Auflösung im sub-Mikrometerbereich. Sie erweitern somit das Gebiet der dynamischen Lichtstreuung in evaneszenter Geometrie, bei dem bislang nur die evanescent wave dynamic light scattering (EWDLS) - Technik zur Verfügung stand. Bei der EWDLS-Technik wird das evaneszente Feld der Totalreflexion als kohärenter Lichtstrahl für die dynamische Lichtstreuung verwendet. Ein Vergleich mit der EWDLS-Technik zeigt ein stark erhöhtes Signal/Rausch-Verhältnis bei den neu entwickelten Techniken aufgrund der resonanten Anregung. Zusätzlich ist es sowohl bei der REDLS- als auch bei der WEDLS-Technik möglich Grenzflächenmodifikationen und damit z.B. Adsorptionsprozesse zu detektieren. Der Einfluss einer Grenzfläche auf die Diffusion von PS-Latex-Partikeln wurde untersucht. Die Grenzfläche bestand im Fall der REDLS-Technik aus Gold, bei der WEDLS-Technik aus PMMA. Die Funktionsweise und die Gültigkeit der neu entwickelten Techniken wurde mit Hilfe von PS-Latex-Partikeln mit hydrodynamischen Radien von R =11nm bis hin zu R=204nm demonstriert.

Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Relaxation of selective constraints causes independent selenoprotein extinction in insect genomes

BACKGROUND: Selenoproteins are a diverse family of proteins notable for the presence of the 21st amino acid, selenocysteine. Until very recently, all metazoan genomes investigated encoded selenoproteins, and these proteins had therefore been believed to be essential for animal life. Challenging this assumption, recent comparative analyses of insect genomes have revealed that some insect genomes appear to have lost selenoprotein genes. METHODOLOGY/PRINCIPAL FINDINGS: In this paper we investigate in detail the fate of selenoproteins, and that of selenoprotein factors, in all available arthropod genomes. We use a variety of in silico comparative genomics approaches to look for known selenoprotein genes and factors involved in selenoprotein biosynthesis. We have found that five insect species have completely lost the ability to encode selenoproteins and that selenoprotein loss in these species, although so far confined to the Endopterygota infraclass, cannot be attributed to a single evolutionary event, but rather to multiple, independent events. Loss of selenoproteins and selenoprotein factors is usually coupled to the deletion of the entire no-longer functional genomic region, rather than to sequence degradation and consequent pseudogenisation. Such dynamics of gene extinction are consistent with the high rate of genome rearrangements observed in Drosophila. We have also found that, while many selenoprotein factors are concomitantly lost with the selenoproteins, others are present and conserved in all investigated genomes, irrespective of whether they code for selenoproteins or not, suggesting that they are involved in additional, non-selenoprotein related functions. CONCLUSIONS/SIGNIFICANCE: Selenoproteins have been independently lost in several insect species, possibly as a consequence of the relaxation in insects of the selective constraints acting across metazoans to maintain selenoproteins. The dispensability of selenoproteins in insects may be related to the fundamental differences in antioxidant defense between these animals and other metazoans.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Percolation transition and the onset of nonexponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in two and three dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the large scale effects of frustration, present below the percolation threshold. Moreover, these results are consistent with the picture suggested by Campbell et al. [J. Phys. C 20, L47 (1987)] in the space of configurations.

Relaxation dynamics in suspensions of ferromagnetic particles

We have studied the relaxation dynamics of a dilute assembly of ferromagnetic particles in suspension. A formalism based on the Smoluchowski equation, describing the evolution of the probability density for the directions of the magnetic moment and of the axis of easy magnetization of the particles, has been developed. We compute the rotational viscosity from a Green-Kubo formula and give an expression for the relaxation time of the particles which comes from the dynamic equations of the correlation functions. Concerning the relaxation time for the particles, our results agree quite well with experiments performed on different samples of ferromagnetic particles for which the magnetic energy, associated with the interaction between the magnetic moments and the external field, or the energy of anisotropy plays a dominant role.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Nitric oxide synthesis and biological functions of nitric oxide released from ruthenium compounds

During three decades, an enormous number of studies have demonstrated the critical role of nitric oxide (NO) as a second messenger engaged in the activation of many systems including vascular smooth muscle relaxation. The underlying cellular mechanisms involved in vasodilatation are essentially due to soluble guanylyl-cyclase (sGC) modulation in the cytoplasm of vascular smooth cells. sGC activation culminates in cyclic GMP (cGMP) production, which in turn leads to protein kinase G (PKG) activation. NO binds to the sGC heme moiety, thereby activating this enzyme. Activation of the NO-sGC-cGMP-PKG pathway entails Ca2+ signaling reduction and vasodilatation. Endothelium dysfunction leads to decreased production or bioavailability of endogenous NO that could contribute to vascular diseases. Nitrosyl ruthenium complexes have been studied as a new class of NO donors with potential therapeutic use in order to supply the NO deficiency. In this context, this article shall provide a brief review of the effects exerted by the NO that is enzymatically produced via endothelial NO-synthase (eNOS) activation and by the NO released from NO donor compounds in the vascular smooth muscle cells on both conduit and resistance arteries, as well as veins. In addition, the involvement of the nitrite molecule as an endogenous NO reservoir engaged in vasodilatation will be described.